When I NIntegrate the Integrand with the particular parameter showing below the Kernel **crash** without any Message.

But if I change the “range” parameter a little bit, the Kernel won’t crash. The crash problem seems to occur only under certain parameters.

Because I want to make a density plot of the integral as a function of the parameters, this crash problem under certain parameters always breaks the density plot process.

PS: This crash problem happens both on Mac and Win10

```
(*Integrand*)
expression1 = {{-0.03783737745791316` +
52.07594879537986` (k1^2 + k2^2) -
0.0006566020385220937` (GothicCapitalB)3,
-0.00020215783672119025` ((GothicCapitalB)1 -
I (GothicCapitalB)2), (0.` + 0.` I) +
1/2 (273.35324964239567` (k1 - I k2)^3 -
22.668570452264646` (k1 + I k2)^3),
0.` + I (k1 - I k2) (-1.0301133331497063` -
370.16816003256605` (k1^2 +
k2^2))}, {-0.00020215783672119025` ((GothicCapitalB)1 +
I (GothicCapitalB)2), -0.03783737745791316` +
52.07594879537986` (k1^2 + k2^2) +
0.0006566020385220937` (GothicCapitalB)3,
0.` - I (k1 + I k2) (-1.0301133331497063` -
370.16816003256605` (k1^2 + k2^2)), (0.` + 0.` I) +
1/2 (22.668570452264646` (k1 - I k2)^3 -
273.35324964239567` (k1 + I k2)^3)}, {(0.` + 0.` I) +
1/2 (-22.668570452264646` (k1 - I k2)^3 +
273.35324964239567` (k1 + I k2)^3),
0.` + I (k1 - I k2) (-1.0301133331497063` -
370.16816003256605` (k1^2 + k2^2)), -0.03304414880767263` +
95.54303239292248` (k1^2 + k2^2) -
0.0015031216532114644` (GothicCapitalB)3,
-0.00017807130082869512` ((GothicCapitalB)1 -
I (GothicCapitalB)2)}, {0.` -
I (k1 + I k2) (-1.0301133331497063` -
370.16816003256605` (k1^2 + k2^2)), (0.` + 0.` I) +
1/2 (-273.35324964239567` (k1 - I k2)^3 +
22.668570452264646` (k1 +
I k2)^3), -0.00017807130082869512` ((GothicCapitalB)1 +
I (GothicCapitalB)2), -0.03304414880767263` +
95.54303239292248` (k1^2 + k2^2) +
0.0015031216532114644` (GothicCapitalB)3}};
expression2 = {{104.15189759075972` k1s, 0,
1/2 (820.059748927187` (k1s - I k2)^2 -
68.00571135679394` (k1s + I k2)^2), (0.` -
740.3363200651321` I) k1s (k1s - I k2) +
I (-1.0301133331497063` -
370.16816003256605` (k1s^2 + k2^2))}, {0,
104.15189759075972` k1s, (0.` + 740.3363200651321` I) k1s (k1s +
I k2) - I (-1.0301133331497063` -
370.16816003256605` (k1s^2 + k2^2)),
1/2 (68.00571135679394` (k1s - I k2)^2 -
820.059748927187` (k1s + I k2)^2)}, {1/
2 (-68.00571135679394` (k1s - I k2)^2 +
820.059748927187` (k1s + I k2)^2), (0.` -
740.3363200651321` I) k1s (k1s - I k2) +
I (-1.0301133331497063` - 370.16816003256605` (k1s^2 + k2^2)),
191.08606478584497` k1s,
0}, {(0.` + 740.3363200651321` I) k1s (k1s + I k2) -
I (-1.0301133331497063` - 370.16816003256605` (k1s^2 + k2^2)),
1/2 (-820.059748927187` (k1s - I k2)^2 +
68.00571135679394` (k1s + I k2)^2), 0,
191.08606478584497` k1s}};
expression3 = {{104.15189759075972` k2s, 0,
1/2 ((0.` - 820.059748927187` I) (k1 - I k2s)^2 - (0.` +
68.00571135679394` I) (k1 +
I k2s)^2), -1.0301133331497063` - (0.` +
740.3363200651321` I) (k1 - I k2s) k2s -
370.16816003256605` (k1^2 + k2s^2)}, {0,
104.15189759075972` k2s, -1.0301133331497063` + (0.` +
740.3363200651321` I) (k1 + I k2s) k2s -
370.16816003256605` (k1^2 + k2s^2),
1/2 ((0.` - 68.00571135679394` I) (k1 - I k2s)^2 - (0.` +
820.059748927187` I) (k1 + I k2s)^2)}, {1/
2 ((0.` + 68.00571135679394` I) (k1 - I k2s)^2 + (0.` +
820.059748927187` I) (k1 +
I k2s)^2), -1.0301133331497063` - (0.` +
740.3363200651321` I) (k1 - I k2s) k2s -
370.16816003256605` (k1^2 + k2s^2), 191.08606478584497` k2s,
0}, {-1.0301133331497063` + (0.` + 740.3363200651321` I) (k1 +
I k2s) k2s - 370.16816003256605` (k1^2 + k2s^2),
1/2 ((0.` + 820.059748927187` I) (k1 - I k2s)^2 + (0.` +
68.00571135679394` I) (k1 + I k2s)^2), 0,
191.08606478584497` k2s}};
HamiltCompiled =
Compile({{k1, _Real}, {k2, _Real}, {(GothicCapitalB)1, _Real}, {
(GothicCapitalB)2, _Real}, {(GothicCapitalB)3, _Real}},
Evaluate(expression1),
CompilationOptions -> {"ExpressionOptimization" -> True});
Dk1HamiltCompiled =
Compile({{k1s, _Real}, {k2, _Real}, {(GothicCapitalB)1, _Real}, {
(GothicCapitalB)2, _Real}, {(GothicCapitalB)3, _Real}},
Evaluate(expression2),
CompilationOptions -> {"ExpressionOptimization" -> True});
Dk2HamiltCompiled =
Compile({{k1, _Real}, {k2s, _Real}, {(GothicCapitalB)1, _Real}, {
(GothicCapitalB)2, _Real}, {(GothicCapitalB)3, _Real}},
Evaluate(expression3),
CompilationOptions -> {"ExpressionOptimization" -> True});
OccupiedCurvatureCompiled((Mu)_?NumericQ, k1_?NumericQ,
k2_?NumericQ, (GothicCapitalB)1_, (GothicCapitalB)2_,
(GothicCapitalB)3_) :=
Block({Mx1, Mx2, values, vectors, curvaturesList},
{values, vectors} =
Eigensystem@
HamiltCompiled(k1,
k2, (GothicCapitalB)1, (GothicCapitalB)2,
(GothicCapitalB)3);
{values, vectors} = {values((#)), vectors((#))} &(
Ordering@values);
Mx1 = vectors(Conjugate).(Dk1HamiltCompiled(k1,
k2, (GothicCapitalB)1, (GothicCapitalB)2,
(GothicCapitalB)3)).vectors(Transpose);
Mx2 = vectors(Conjugate).(Dk2HamiltCompiled(k1,
k2, (GothicCapitalB)1, (GothicCapitalB)2,
(GothicCapitalB)3)).vectors(Transpose);
curvaturesList =
Re(I Total((# - #(Transpose)))) &(
Mx1*Mx2(Transpose)*
Table(If(n1 == n2, 0, 1/(values((n1)) - values((n2)))^2), {n1,
1, 4}, {n2, 1, 4}));
curvaturesList.Boole@Thread(values < (Mu))
);
```

```
(*No Crash*)
With({range =
0.0006` +
0.00025*19.`, (Mu) = -0.034637500000000015`, (GothicCapitalB)1 =
0., (GothicCapitalB)2 = 19.`, (GothicCapitalB)3 = 0.},
NIntegrate(
OccupiedCurvatureCompiled((Mu), k1,
k2, (GothicCapitalB)1, (GothicCapitalB)2, (GothicCapitalB)3),
{k1, -range, range}, {k2, -range, range}, MinRecursion -> 2,
PrecisionGoal -> 3, AccuracyGoal -> 3))
```

```
(*Crash*)
With({range =
0.0005` +
0.00025*19.`, (Mu) = -0.034637500000000015`, (GothicCapitalB)1 =
0., (GothicCapitalB)2 = 19.`, (GothicCapitalB)3 = 0.},
NIntegrate(
OccupiedCurvatureCompiled((Mu), k1,
k2, (GothicCapitalB)1, (GothicCapitalB)2, (GothicCapitalB)3),
{k1, -range, range}, {k2, -range, range}, MinRecursion -> 2,
PrecisionGoal -> 3, AccuracyGoal -> 3))
```